Synopsis

Recently, low frequency (LF) magnetic resonance electrical conductivity imaging by means of oscillating gradient fields is reported to be infeasible. In these studies, LF phase measurements are modeled with radio frequency (RF) leakage due to geometric shifts in MR images. Although RF leakage is related with conductivity, we have not come across a conductivity image reconstructed using this model. In this study, LF conductivity imaging is evaluated for an MRI pulse sequence including multiple gradient pulses. Geometric shifts are evaluated by focusing on the MR magnitude. A procedure is proposed for the reconstruction of conductivity, based on LF phase measurements.

Introduction

Methods

Using Maxwell’s equations, fundamental equation of oscillating gradient based LF conductivity imaging can be derived² as

$$\sigma=\nabla^2{B_{sz}}/(\mu_o\partial{B_{pz}}/\partial{t}), [1]$$

where $B_{pz}$ and $B_{sz}$ are the z components of the primary and the secondary magnetic fields created by the gradients and LF induced eddy current (${{\bf J}_{LF}}$), respectively. Considering a spin-echo pulse sequence with multiple SS gradient (G_z) and 180^o RF pulses as shown in Figure 1³, $B_{sz}$ and $\Phi_{LF}$ are related as

$$\Phi_{LF}=2(N_s-0.5)\gamma{B_{sz}(i,j)}t_r, [2]$$

where $N_s$ is the number of soft 180^o RF pulses, $\gamma$ is the gyromagnetic ratio of hydrogen, and $t_r$is the ramp duration. $B_{pz}$ is determined considering gradient strength ($GS$), gradient iso-center and slice location. To obtain $B_{sz}$, $\Phi_{LF}$ measurements are denoised and scaled. Geometric information is obtained by applying edge detection to MR magnitude image. Quadratic polynomials in horizontal ($x$) and vertical ($y$) directions are fitted to $B_{sz}$ to obtain filtered $B_{sz}$images. Finally, $\sigma$ is reconstructed by simplifying Eq. [1] as

$$\sigma=(\frac{\partial^2{B_{sz-x}}}{\partial{x^2}}+\frac{\partial^2{B_{sz-y}}}{\partial{y^2}})/(\mu_o\partial{B_{pz}}/\partial{t}), [3]$$

where $B_{sz-x}$ and $B_{sz-y}$are the filtered images. In order to investigate $\Phi_{RF-leak}$ due to geometric shifts, we focus on MR magnitude images.

The pulse sequence in Figure 1 is realized on a 3T MRI scanner (Magnetom Trio, Siemens AG, Erlangen, Germany). Transverse (xy) slice with a thickness of 5 mm is selected. G_z is applied with $GS=4.8$ mT/m and $N_s=21$. Field of view is 25×25 cm² with spatial sampling of 128×128 pixels. By applying the pulse sequence twice with positive and negative G_z polarities and taking the difference of resultant $\Phi$ distributions $\Phi_{LF}$ is obtained^1-3. A cylindrical Plexiglas phantom with a diameter of 19 cm and a height of 10 cm is used as shown in Figure 2. The phantom is filled with a solution of 0.55 g NaCl and 0.05 g CuSO₄ in 100 ml distilled water. A cylindrical inhomogeneity with a diameter of 4.8 cm and a height of 10 cm is located inside the phantom. The inhomogeneity is composed of 0.8 g NaCl, 0.05 g CuSO₄, 1 g Agar and Tx151 in 100 ml distilled water. Conductivity of the background and the inhomogeneity are 0.75 S/m and 1.2 S/m, respectively.

Results

Discussion and Conclusion

Investigation of $M^+$, $M^-$, and $\Delta{M}$ images reveals the intensity differences. Characteristics of $M^+$ and $M^-$ profiles are the same at the boundary pixels. $M^+$ and $M^-$ profiles have the maximum and the minimum at the same locations. We can conclude that $\Delta{M}$ is due to intensity differences rather than geometric shifts. $\Phi_{LF}$ has quadratic characteristics in the background and the inhomogeneity different from the $\Phi_{RF-leak}$ model of $\Phi_{LF}$ distributions in ^1-2 which have linear spatial characteristics. Reconstruction of $\sigma$ images with Eq. [1] and the reported $\Phi_{RF-leak}$ distributions in ^1-2 may not be possible. Reconstructed $\sigma$ image is a rough approximation of the true $\sigma$ distribution of the phantom. Boundary artifacts are observed due to $\nabla\sigma=0$ assumption during derivation of Eq. [1].

We think that switching gradient based LF conductivity imaging should be investigated with MRI pulse sequences including multiple gradient pulses. By this way, $\Phi_{LF}$ measurements can be increased. Magnetohydrodynamic force created by the interaction of ${{\bf J}_{LF}}$ and static magnetic field ($B_o$) of the MRI scanner⁴, diffusion, and drift effects may be sufficiently large to dominate the $\Phi_{LF}$ measurements, which are close to the phase measurement noise level of MRI scanners⁵. These flow effects should be investigated in detail in order to master the physics of $\Phi_{LF}$ measurements even with homogenous Agarose gel phantoms.

Acknowledgements

References

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